共享结构复用网络的潜在空间模型
Latent space models for multiplex networks with shared structure
摘要：
潜空间模型经常用于单层网络的建模，包括许多流行的特殊情况，如随机块模型和随机点积图。然而，它们并不适合更复杂的网络结构，这在实践中变得越来越普遍。在这里，我们提出了一个新的潜在空间模型的多重网络：多个，异构网络上观察到的共享节点集。多重网络可以表示具有共享节点标签的网络样本、随时间演进的网络或具有多种类型的边的网络。我们的模型的关键特征是，它从数据中学习网络结构中有多少是在层之间共享的，并在适当的情况下跨层共享信息。我们建立了可识别性，开发了一个拟合过程，结合使用凸优化与核规范的惩罚，并证明了恢复的潜在位置，只要有足够的共享和个人的潜在子空间之间的分离的保证。我们比较了模型的竞争方法在文献中的模拟网络和一个多元化的网络描述的全球农产品贸易。
英文摘要：
Latent space models are frequently used for modeling single-layer networks and include many popular special cases, such as the stochastic block model and the random dot product graph. However, they are not well-developed for more complex network structures, which are becoming increasingly common in practice. Here we propose a new latent space model for multiplex networks: multiple, heterogeneous networks observed on a shared node set. Multiplex networks can represent a network sample with shared node labels, a network evolving over time, or a network with multiple types of edges. The key feature of our model is that it learns from data how much of the network structure is shared between layers and pools information across layers as appropriate. We establish identifiability, develop a fitting procedure using convex optimization in combination with a nuclear norm penalty, and prove a guarantee of recovery for the latent positions as long as there is sufficient separation between the shared and the individual latent subspaces. We compare the model to competing methods in the literature on simulated networks and on a multiplex network describing the worldwide trade of agricultural products.
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